Abstarct: Chaos synchronization is to drive a chaotic system namely slave to mimic the behavior of another chaotic system namely master by imposing control signals. In this thesis, we study the synchronization of uncertain chaotic systems using optimal robust control, which is achieved by the Linear Quadratic Regulator (LQR). This approach is to transform a robust control problem into an optimal control problem. The nonlinear optimal controls are usually obtained by solving the Hamilton–Jacobi–Bellman (HJB) equations, which its solution is quite complicated and time-consuming. An alternative approach to solve the nonlinear optimal control problem is the State-Dependent Riccati Equation (SDRE). In this method, the corresponding equations are described like a Linear Quadratic Regulator (LQR) problem. Thus, the solution of the robust control can be obtained by the solution of LQR problem. In this thesis, four different examples are demonstrated to show the performance of the proposed control approach. The results illustrate that the proposed approach can effectively decrease the error of chaos synchronization. Chaos, Synchronization, Robust control, Linear Quadratic Regulator